The first phrase (to send a link by Skype) always comes to my mind when I want to convey the idea "to send a link via Skype". But then I bite back and say "to send a link on Skype" (since I know the latter is correct, and the former is the phrase I'm unsure of).

You could argue that "on" and especially "in" (as in "in a program") could be used, but as Thelb4 suggests "by," "via," and "over" would sound natural. Personally, I'd be likely to use "by" and "through."